Summary
The authors propose a causal representation learning method that can learn the latent variables and causal graphs over them on time series data under an assumption, namely single-parent decoding.
Strengths
1. The proposed method can learn the nonlinearity in the relationships between latent variables and the mapping from latent to observational variables.
2. The authors prove the identifiability of both latent representation and its causal graph.
3. The authors conduct experiments on the simulated dataset, compared with some baseline algorithms.
4. The real-world experiment is interesting, and the dataset is high-dimensional, showing that the proposed algorithm works well with high-dimensional observations.
Weaknesses
1. The single-parent decoding assumption seems to be a very strong assumption on time series data, given that time series data often exhibit autocorrelation, which is indeed a key characteristic of such data. To be more precise, there are typically causal relationships among observational data, resulting in multiple parents.
2. The paper lacks an explicit assumption section that systematically outlines all the assumptions required in the algorithm. Examples of such assumptions may include causal stationarity, the absence of instantaneous causal relationships for guaranteed identifiability, and others.
3. The content of experiment plots in Fig. 2-3 is not very informative as the various conditions are limited to just two or three distinct values.
4. The experimental results do not convincingly demonstrate that the proposed method has significant advantages over the baseline algorithm, as suggested in the main paper, where it states that "Varimax-PCMCI performs slightly better than CDSD in most conditions, except for more challenging cases...". The "more challenging cases" specifically involve only two synthetic datasets with time lags ($\tau = 3$) and dense graphs ($p = 0.3$). Would it be feasible to conduct additional experiments with larger values of $\tau$ and $p$ to gather more conclusive evidence? Furthermore, the paper lacks specific details in the plots for the nonlinear cases, which represent the advantageous scenarios for the proposed method. For example, the paper only includes Fig.2b for nonlinear latent dynamics cases with various samples and only includes Fig.3b for nonlinear decoding cases with different densities $p$.
5. The number of baseline algorithms is limited. Could you please briefly explain why Mapped-PCMCI mentioned in the related work has not been applied as another baseline?
Questions
1. In equation (3), the observational variable given its latent parent follows a normal distribution. Is this an assumption that was not explicitly mentioned in the paper?
2. In equation (4), what is the definition of $p(Z^{t}|Z^{<t})$ for $t\leq\tau$?
3. In the synthetic experiment section, is there any reason that the case of nonlinear dynamics and nonlinear decoding has not been discussed?
4. In Fig.2, $\tau$ varies from 1 to 3, and the SHD of the proposed method first increases and then decreases. Could you briefly explain why this happened? The relation between the performance of the method and $\tau$ is not apparent unless further investigation includes additional values of $\tau$, such as exploring how the SHD changes for $\tau=4, 5, \ldots$.
5. In Fig.2b, the time issue for Varimax-PCMCI is reasonable, however, is it feasible to conduct more experiments for $T<1000$? If the computation time for $T=5000$ is excessive, could experiments be performed for $T=1500$ or $T=2000$ for Varimax-PCMCI, thereby enabling a more comprehensive comparison?
6. When comparing the proposed method with iVAE and DMS, the constraint on $W$ is not applied to both baselines. How does this modification lead to a fairer comparison, given that the constraint ensures that the single-parent decoding assumption holds?
7. Is there any reason to apply linear dynamics and linear decoding in the real-world dataset, but not other versions?
8. In Fig.5a, does the statement "The groups are colored and numbered based on the latent variable to which they are related" suggest that the small circles sharing the same color correspond to the same latent parents? If so, given that the color of clusters 39, 41, 40 seems the same to me, does this mean they are clustered based on the same latent parents?
9. With $d_z=50$, could you briefly explain how to get the causal graph in Fig.5c? Is it possible for the estimated causal graph to contain cycles? For instance, could it be the case that $Z_1^t \rightarrow Z_2^{t+1}$ and $Z_2^t \rightarrow Z_1^{t+1}$?
Rating
3: reject, not good enough
Confidence
3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.